Here is some additional information affirming your answer.
The words with no consecutive equal letters are so-called Smirnov words. If you are curious about them you might have a look at example III.24 in Analytic Combinatorics which explains some properties of them.
We count the number of Smirnov words of length $n$ with the help of formal power series. The coefficients of $z^n$ give the number of words of length $n$.
It turns out that the power series of Smirnov words with $26$ letters is
The coefficients of $z^n$ were calculated with the help of Wolfram Alfa.
We observe, the number of Smirnov words of length $6$ is